Recognizing Bias in Graphs

Transcription

1 Name Date Class WORKSHEET 28 Recognizing Bias in Graphs Graphs can be used to display your data at a glance. However, graphs can distort your results if you are not careful. The picture that results may not be objective, or without bias or distortion. Look at the first graph. How Much Rain Really Fell? In the graph below, it appears as though March had drastically more rainfall compared with an average month. But did that really happen? This Year s Rainfall Versus Average Rainfall Amount of rainfall (cm) January February March Month Average rainfall This year s rainfall Wait! March s rainfall was only 0.4 cm above average. On the graph, that looks like a large increase. On the ground, a 0.4 cm increase is not that much. This graph is biased because it exaggerates the difference between the two lines. Because the interval between 27.8 cm to 28.7 cm on the y-axis is so small, the difference in rainfall seems very large and noticeable. If you increase the interval between numbers on the y-axis, the scale becomes larger. That makes the difference between the two lines smaller, as shown below. Amount of rainfall (cm) This Year s Rainfall Versus Average Rainfall January February March Month Average rainfall This year s rainfall 68 HOLT SCIENCE AND TECHNOLOGY

2 Name Date Class Recognizing Bias in Graphs, continued Refer to the graphs on the previous page to answer the following questions: 1. What is the range of values on the y-axis in the second graph? 2. How does the difference between the two lines in the second graph compare with the difference between the two lines in the first graph? Which graph is a more accurate picture of the data? Explain. A Matter of Scale Here is another example of how the choice of the scale can alter a graph. In an experiment, seven students tried to mix a solution of salt water so that its concentration would be exactly 7.00%. When the teacher tested the concentration of their solutions, he got the following results: Concentrations of Students Solutions Name Bruno Cali Shaun Chazz Jessie Janet Tonya Concentration 7.02% 6.99% 7.00% 7.08% 6.97% 7.01% 6.99% The teacher created the following graph to show the students results: Concentration % Concentrations of Students Solutions 6.0 Bruno Cali Shaun Chazz Jessie Janet Tonya Student Does this graph give you a clear picture of how the concentrations varied? Not really. The bars look so much alike that it s hard to tell the differences between them. SCIENCE SKILLS WORKSHEETS 69

3 Name Date Class Recognizing Bias in Graphs, continued Suppose the teacher decreased the scale of the y-axis. The graph would then look like the one below. The variation in the students results looks much greater, even though it hasn t changed. This graph makes it easier to see the small differences. 7.1 Concentrations of Students Solutions Concentration % Bruno Cali Shaun Chazz Jessie Janet Tonya Student Graphs with an Attitude The data in the chart below were recorded by a student measuring the thickness of four rock layers. Thickness of Rock Layers Layer Thickness Using the above data, create two graphs in the space below. First show how similar the measurements are. (Hint: Make the scale of the y-axis larger. This makes the difference between the measurements seem smaller.) In your second graph, emphasize the fact that layer C was slightly thicker than the other layers. Your Graphs: A B C D HOLT SCIENCE AND TECHNOLOGY

4 Name Date Class Recognizing Bias in Graphs, continued Identifying Bias on Your Own Graph 1 Height (cm) Height of Test Plants 1. This graph shows that test plant D grew much taller than the other plants. How is this information misleading? A B C D E Test plant Graph 2 Kendra's score Kendra s Scores in Science Class for Each Quarter st 2nd 3rd 4th Quarter 2. This graph shows that Kendra received a much lower grade in science class during the fourth quarter. Do you think what appears to be such a large drop in her grades should worry Kendra? Explain your reasoning. SCIENCE SKILLS WORKSHEETS 71

5 Name Date Class WORKSHEET 29 Making Data Meaningful The following sentences use the word average in different ways: He was just an ordinary, average guy. The average volume of the six solids was 3.2 cm What is different about the way average is used in each sentence? 2. What is similar about the way average is used in each sentence? What Does It All Mean? Because average can be used in different ways, scientists use the word mean instead. In this sense, mean is the same as a mathematical average. For instance, to find the mean height of seven students, you add up their individual heights and divide the sum by seven, the number of students. Suppose the seven students above are third-graders who live in Charlotte, North Carolina. If you wanted to find the mean height of third-graders in Charlotte, you could do one of the following two things: You could measure the height of every single third-grader in Charlotte, and then calculate the population mean. This would take a long time because there are thousands of third-graders in Charlotte. The population mean refers to a mathematical average that has been calculated based on all of the available data. You could measure the height of several third-graders in certain areas and calculate the sample mean. The sample mean refers to a mathematical average that has been calculated based on only some (a sample) of the available data. The sample mean is an estimate of the population mean. 3. When do you think it is more appropriate to calculate a sample mean? Can you think of any problems with using a sample mean? 72 HOLT SCIENCE AND TECHNOLOGY

6 Name Date Class Making Data Meaningful, continued 4. When do you think it is more appropriate to calculate a population mean? Can you think of any problems with using a population mean? Mode, Median, and Range Mode, median, and range are other important mathematical tools for interpreting data. The mode is the value that occurs most often in a set of data. For example, imagine you are counting the number of slices of pepperoni on certain pieces of pizza. Following are the outcomes for 10 pieces: Number of Pepperoni Slices per Piece of Pizza Pizza piece Pepperoni slices A B C D E F G H I J Which number occurs most often in the data set? By counting how many times each number appears, you find that 5 appears most often. Therefore 5 is the mode. It is possible to have more than one mode in a set of data. If two values tie for the most occurrences, the data set has two modes. For example, if there had been one more 2 in the data above, the modes would have been 5 and 2. The median is the middle value of a set of data listed in numerical order. If a set of data contains an even number of items, it will have two middle numbers. In this case, to find the median, you average the two middle numbers. Let s find the median for the data set listed above. First, put the data in numerical order, from least value to greatest value Notice there are two middle numbers in this set, 3 and 5. We must average them then to get the median; (3 + 5) 2 = 4, so 4 is the median! The range is the difference between the greatest number and the smallest number in the data set. Range shows how much the data set varies. Let s find the range of the set of data above. The greatest number is 6, and the smallest number is 1. To find the difference, we subtract 1 from The range for the data set is 5, so the data vary over 5 values. SCIENCE SKILLS WORKSHEETS 73

7 Name Date Class Making Data Meaningful, continued Your Turn Find the statistical measures for the following sets of data: 5. 3, 5, 7, 9, 5, 6, 4, 3, 2, 22 a. Mean b. Mode c. Median d. Range 6. 4, 19, 3, 19, 4 a. Mean b. Mode c. Median d. Range 74 HOLT SCIENCE AND TECHNOLOGY